Create Object along three curves
Sverchok

You can build the geometry starting from the curves interactively by accessing their vertex coordinates with the Sverechok add-on.

As you can see in the image sequence below, this will allow you to move each curve in object mode or it's control points in edit mode and transform the resulting surface by simply updating the script.



For the following, example I choose to build an 3-points-arch for the sake of semplicity as Sverchock has a built in node that is able to create an arc from a given points triplet, but with more effort you can surely achieve whatever result. 



On the right of the image below you can see three Object input nodes, one for each curve, followed by a Matrix apply node to get the absolute coordinates of the vertices. As they are stored in separate lists, you'll have to join them. By enabling Mix option we esure that all the first vertices of each curve is bundled with the other in the array.

Then you just have to set the arbitrary resolution of the arc and place an output node (Viewer Draw in this case).



In order to get a full surface we should add some nodes. In this case I picked a Cylinder's polygons indices after filtering out the faces that were connecting the two curves on bottom and joining this data with the vertices coming out from the 3 Point Arc node.



The images above are showing a blue surface because it's just the add-on preview, no "real" geometry has benn created yet, as before we must define also the edges of the surface.

As did for the polygons, I filtered out the edges (they need some further math tricks) and then added a Bmesh viewer to bake the surface in the scene.

Here's the final node setup:





Note:
The nodetree is expecting curves made by the same amount of vertices (there is a node where you should input that). Keep them with the same number of control points &amp; resolution. Same thing if you choose to input meshes instead of curves.